CHAPTER 4 MATHEMATICAL MODELING AND SIMULATION

Transcription

1 49 CHAPTER 4 MATHEMATICAL MODELING AND SIMULATION 4.1 INTRODUCTION Mathematical modeling is an approach in which, practical processes and systems can generally be simplified through the idealizations and approximations in the form of system of equations to solve a problem. Also, it enables us to understand and predict the behaviour and characteristics of thermal systems. Once a model is formulated, it can be subjected to a range of operating conditions and design variations. This chapter deals with the modeling and simulation of an automobile air-conditioning system operated with R12 and the proposed mixture (M09) as the refrigerant. Automobile air-conditioning systems work basically on the principle of the vapor compression refrigeration cycle. The theoretical vapor compression cycle consists of an isentropic compression, isenthalpic expansion, and isobaric evaporation and condensation. The four major components used are the compressor, thermostatic expansion valve, evaporator and condenser. These components are simulated separately and integrated to simulate the entire system using MATLAB software. REFPROP 7.0 is used to evaluate the refrigerant properties. The simulation model is based on the components actually present in the experimental test rig as detailed in Appendix 1.

2 MODELING AND SIMULATION OF EVAPORATOR A mathematical model is created to predict the automobile airconditioning evaporator performance under steady state conditions. The evaporator used in the experimental test rig is a fin and tube evaporator, 7 rows deep with three circuits. The total number of tubes is 32 and the dimensions pertaining to the tube and fin, and the overall dimensions are detailed in Figure 4.1. Figure 4. 1 Evaporator tube circuit layout

3 Modeling of evaporator evaporator: The following assumptions have been made in simulation of Refrigerant flow was one-dimensional. The pressure drop measured across the evaporator is uniformly distributed. The heat transfer from refrigerant to atmosphere through the bend regions was negligible. The total air delivered by the fan was equally divided over the entire tube length. Pressure of vapor and liquid was equal at all points in the cross section of any tube. The effect of the oil present in the refrigerant is negligible. The tubes are either fully dry or fully wet. The water film on the wet nodes is assumed to be of negligible thickness, and the heat carried away by the drainage of the condensate is ignored. The refrigerant side and airside are modeled separately. Further, the evaporator is divided into a superheated region and two-phase region. When the evaporator performs sensible cooling, the surface temperature is used to estimate the heat transfer between the refrigerant and the air. When the evaporator is cooling and dehumidifying, the water film (condensate) temperature on the coil surface is used for calculating the heat transfer. Though the evaporator tube layout is a cross counter flow arrangement, and the number of rows is seven, it can be assumed to be a counter flow arrangement (more than three rows can be assumed as counter flow

4 52 (Mcquistion and Parker 1994, Stevens 1957, Kays and Crawford 1993). The entire tube length of the evaporator is segregated into small control volumes of known length (2 mm) as shown in Figure 4.2 (Vardhan 1998). Figure 4.2 Single tube - counter flow heat exchanger Figure 4.3 shows the dry and wet zones for airside, and saturated and superheated region for the refrigerant side. When the analysis is done in the direction of airflow, control volume 1 will be the first segment of contact for air and it will be the last segment of contact for refrigerant. For the refrigerant, the inlet pressure is given and with the pressure drop already known from the experimental study, the outlet pressure can be calculated. Since, the evaporator superheat is initialized first, the refrigerant outlet temperature is also known. The evaporator inlet air temperature is the return air temperature from the cabin, which is held constant at 27C. Therefore, Tai and Tro as seen in Figure 4.3 are known. From these temperatures and the available geometry of the heat exchanger, the surface temperature can be found by establishing a heat balance between air and refrigerant side. From the surface temperature, the heat transferred in that control volume and the outlet conditions can be determined. These outlet conditions will be supplied as the inlet conditions for the second control volume. The surface temperature is compared with the dew point temperature of the air at the evaporator inlet. If the surface temperature is above the dew point temperature, condensation of moisture will not take place. This procedure is repeated for other control

5 53 volumes until the surface temperature is less than dew point temperature of the entering air. The length required for the superheated region is calculated. Figure 4.3 Dry and wet zones in the counter flow heat exchanger From this portion of the evaporator instead of temperature difference as the driving potential, the enthalpy difference is used as the driving potential. The maximum enthalpy difference is the difference between the enthalpy of air at the point of condensation and the enthalpy of the saturated air corresponding to the refrigerant inlet conditions. Now, for the remaining wet region the ε-ntu method is used for the calculation of the evaporator duty, but with the modified heat transfer coefficient, which includes the condensation of moisture in the air (Equation 4.27). For a counter flow heat exchanger the effectiveness can be related to the number of transfer units (NTU) with the following expression (Kays and London 1964) 1 e NTU (1 C *) 1 C * e NTU (1 C *) (4.1)

6 54 C* C C min (4.2) max In the two phase region, the heat capacity on the refrigerant side approaches infinity and the heat capacity ratio C* tends to zero, the effectiveness for any heat exchanger in the two phase region is expressed as (Kays and London 1964) NTU 1 e (4.3) The equations 4.11 to 4.27 used to calculate the heat exchanger parameters below are referred from Mcquistion and Parker (1994) and Kuppan (2003). The NTU is a function of the overall heat transfer coefficient and is defined as NTU U A C a a (4.4) min The overall heat transfer coefficient accounts for the total thermal resistance between the two fluids. Neglecting the fouling resistance, it is expressed as follows (Mcquistion and Parker 1994) U A 1 1 R sa a Aa r Ar a a w 1 (4.5) R w D o Aa ln Di (4.6) 2 kl Aa Ap Afin (4.7)

7 55 The surface efficiency on the refrigerant side is considered to be unity as there are no fins. To calculate the fin efficiency on the airside, it is necessary to find the equivalent radius of the fin. The empirical relation for the equivalent diameter is given by McQuiston and Parker (1994). D D eq i ( 0.3) 2 (4.8) The coefficients Ψ and β are defined as M (4.9) r L (4.10) M Once the equivalent radius had been determined, the equations for the standard circular fins were used. The length of the fin was much greater than the fin thickness. Therefore, the standard extended surface parameter, m es can be expressed as, 2 a m es (4.11) k fint fin For circular tubes a parameter Φ can be defined as R R ln r r (4.12) The fin efficiency, η fin for a circular fin is a function of m es, D eq and Φ and can be expressed as

8 56 fin tanh( mesr ) (4.13) m r es The total efficiency of the fin η sur, is therefore expressed as sur Afin 1 1 fin (4.14) A a After finding the overall heat transfer coefficient, NTU is determined and from that the efficiency was evaluated. In general, the heat transfer rate is computed using, Q m h (4.15) The effectiveness is expressed by Q (4.16) Q max The maximum heat that could be transferred is given by, the product of the minimum heat capacity and inlet temperature difference of the two fluids. max min ri ai Q C T T (4.17) The actual heat transferred is given by min ri ai Q C T T (4.18) The surface temperature is calculated by equating the airside heat transfer rate and the refrigerant side heat transfer rate and can be expressed as,

9 h A T T h A T T (4.19) ha o a s r r s r 57 T s h A T h A T h A h A ha a a a r r r ha a a r r (4.20) The heat transferred in the superheated region when the surface temperature is more than the dew point temperature i.e., under nondehumidifying conditions, is expressed as (Wang 1990). sh min aei dp Q C T T (4.21) The heat transferred in the superheated region when the surface temperature is less than the dew point temperature, i.e., under dehumidifying conditions, is expressed as, Q m ( h h ) (4.22) sh aei sri The standard extended surface parameter, m es for a fin under dehumidifying conditions can be expressed as, (McQuiston and Parker 1994). 2 hfg W o a Ws m es 1 k fint fin Cpa Ta T (4.23) s (Wang 1990) The outlet enthalpy of the dehumidifying air can be calculated from h h ( h h ) (4.24) ao ai aei sri Evaporator - Heat transfer correlation The mathematical model needs to be supplemented with heat transfer coefficient correlations for both the fluids involved in the heat

10 58 transfer. The airside heat transfer correlations and the refrigerant side heat transfer correlations are presented in this section Air side heat transfer correlations The air side convective heat transfer coefficient is expressed as acp h sa = j * G a*cp a* Ka a 2 3 (4.25) where, TP FS j t 0.14 Rea TPl Do (4.26) The heat transfer coefficient of the humid air is given by (Liang 1999) h ha h sa hfg ( W Ws ) 1 (4.27) Cpa ( Ta Ts ) when there is no dehumidification, then (W-Ws) will be zero and h ha = h as Refrigerant side heat transfer correlations The heat transfer coefficient in the single-phase region is given by the Dittus-Boelter equation. h sh K D v *0.023Re Pr (4.28) hr The heat transfer coefficient in the two-phase region is given by the Klimenko equation (Castro et al 1993). h K K LC v a l tp Reeq Prl l Kl (4.29)

11 59 lcpl where, Prl (4.30) K l and equivalent Reynolds number is given by m r l LC Re eq = 1 xi 1 Aff v l (4.31) where, LC is the Laplace constant. LC l g( ) l v (4.32) Simulation of the evaporator The complete simulation procedure of the evaporator is summarized below. Also, a flow chart depicting the algorithm is detailed in Figure 4.4. Input evaporator dimensions, mass flow rate, P ci, P ei Initialize Q sum, SH, SC, segmental length, etc. Calculate Surface geometrical parameters. Use section-by-section scheme. Calculate air and refrigerant thermo-physical properties. Calculate dimensionless parameters Reynolds number, Prandtl number etc. Calculate j for air and Nu for refrigerant. Check whether surface temperature is less than dew point temperature.

12 60 Start Input Data: Evaporator Geometry, x, m f, P s, T s, ΔP, V a, T aei While T sur > = T dp Dry Region Calculate: μ, ρ, C p, k, Re, Pr, Single phase sensible ht tr. coeff. Dittus Boelter equation C max, C min, η f, U ε, NTU, Q Pressure drop for the segment (Δp seg ) P i = P i + Δp seg, L seg = L seg + dl Q sum = Q sum + Q sh While T sur > = T dp & T ref <T sat Wet Region Calculate: μ, ρ, C p, k, Re, Pr, Single phase sensible ht tr coeff. Dittus Boelter equation Cmax, Cmin, η f, U ε = m a (enthalpy diff), NTU, Q Pressure drop for the segment (Δp seg ) P i = P i + Δp seg, L seg = L seg +dl Super heated Region Q sum = Q sum + Q sh A Figure 4.4 Flow chart for Evaporator simulation

13 61 A While X < = 1 Calculate: μ, ρ, C p, k, Re, Pr, j factor, Heat transfer coefficient humid air Calculate: Heat absorbed for 0.01 quality rise Q tp = f (P i, x i, x o ) = m f * ΔH μ, ρ, C p, k, σ, Re, Pr, for saturated liquid and vapour and Laplace constant Two phase ht.tr. coeff. Klimenko eqn C max, C min, η f, U ε = m a (enthalpy diff), NTU, Q Pressure drop for the segment (Δp seg ) P i = P i Δp seg, L seg = L seg +dl x i = x o x o = x o Check T assumed = T out Two Phase Region Q sum = Q sum + Q tp Print outputs: Stop Figure 4.4 Flow chart for Evaporator simulation (continued)

14 62 If the condition is not satisfied find sensible heat transfer coefficient. If the condition is satisfied find combined heat transfer coefficient and proceed. Determine fin efficiency. Calculate the overall conductance (1/UA). Using ε - NTU method, find effectiveness. Calculate the heat transferred in one section. Calculate the pressure drop in that section. Check for surface - dew point temp and saturation temperature. Once dew point is reached, assume exit temperature of air. Calculate enthalpy difference instead of temperature difference to analyse the heat transfer in the wet region. Proceed to the next section till saturation temperature is reached Find the cumulative length required for the superheat region. Vary quality by 0.1. Calculate the heat transferred and the pressure drop for the remaining length. Calculate the outlet quality and total heat transferred. Find the outlet temperature of the air and check with the assumed temperature. Substitute successively till the convergence is achieved. The deliverables from the evaporator outlet are evaporator outlet temperature, quality and evaporator heat transfer rate.

15 MODELING AND SIMULATION OF CONDENSER Modeling of condenser The following assumptions have been made in simulation of condenser: The pressure drop in the straight tubes is uniform throughout. Refrigerant flow was one-dimensional. The heat transfer from refrigerant to atmosphere through the bends is negligible. The total air delivered by the fan was equally divided over the entire tube length. Pressure of vapor and liquid was equal at all points in the cross section of any tube. The effect of the oil present in the refrigerant is negligible. A mathematical model is created to predict the automobile airconditioning condenser performance under steady state conditions. The condenser used in the experimental test rig is a flat tube serpentine condenser with louver fins and cross flow arrangement. The total number of tubes is 14 and the dimensions pertaining to the tube and fin and the overall dimensions are detailed in Figure 4.5. The refrigerant side and airside are modeled separately. Further, the condenser is divided into a de-superheating region, a two-phase region and a sub-cooled region. The entire tube length of the condenser is separated into small control volumes of known length (2 mm) Condenser - Heat transfer correlation Parker, 1994). The airside heat transfer coefficient is given by (McQuiston and

16 64 Figure 4.5 Cut view of the flat tube automotive condenser with louver fins acp h a = j * G a*cp a* Ka a 2 3 (4.33) G Dh a a Rea a (4.34) The colbourn factor is given by (Castro and Ali, 2000) Rea Rea j = * * (4.35) The heat transfer coefficient of the superheated region is given by (Dittus and Bolter equation)

17 65 h sh K D v *0.023Re Pr (4.36) hr The heat transfer coefficient in the two-phase region is given by (Castro and Ali, 2000) Kl h tp = * 0.05 Re Pr D hr eq l (4.37) 0.5 v l Re Re Re l v eq v l (4.38) The overall heat transfer coefficient is calculated from U A 1 1 R sa a Aa r Ar a a w 1 (4.39) R w D o Aa ln Di (4.40) 2 kl The overall surface area is given by Aa Ap Afin (4.41) The other heat exchanger relations discussed in the evaporator holds good for the condenser too (except dehumidifying correlations) Simulation of the condenser The complete simulation procedure of the condenser is summarized below. A flow chart depicting the calculation procedure is detailed in Figure 4.6.

18 66 Input condenser dimensions; mass flow rate, P ci, P ei. Calculate Surface geometrical parameters. Use section-by-section scheme. Calculate air and refrigerant thermo-physical properties. Calculate dimensionless parameters Reynolds number, Prandtl number etc. Calculate j for air and Nu for refrigerants. Find the heat transfer coefficients for superheated region. Determine fin efficiency. Calculate the overall conductance (1/UA). Using ε - NTU method, find effectiveness. Calculate the heat transferred in one section. Calculate the pressure drop in that section. Proceed with next section till saturation temperature is reached. Find the cumulative length required for the superheat region. Increase the evaporator refrigerant quality in steps of 0.1. Calculate air and refrigerant thermo-physical properties. Calculate dimensionless parameters Reynolds number, Prandtl number etc, for the two-phase region. Calculate j for air and Nu for refrigerants.

19 67 Find the heat transfer coefficients for the two-phase region. Determine fin efficiency. Calculate the overall conductance (1/UA). Using ε - NTU method, find effectiveness. Calculate the outlet quality and heat transferred in one section. Calculate the pressure drop in that section. Proceed with the next section till quality becomes zero. Find the cumulative length required for the two-phase region. Calculate air and refrigerant thermo-physical properties for sub-cooled region. Calculate dimensionless parameters Reynolds number, Prandtl number etc. Calculate j for air and Nu for refrigerants. Find the heat transfer coefficients for sub-cooled region. Determine fin efficiency. Calculate the overall conductance (1/UA). Using ε - NTU method, find effectiveness. Calculate the heat transferred and the pressure drop for the remaining length. Find the net heat transferred and the outlet temperature of the air.

20 68 Start Input Data: Condenser Geometry, m f, P d, T d, ΔP, H d, V a, T aci Calculate: μ, ρ, C p, k, Re, Pr, j factor, Heat transfer coefficient dry air While T i < = T sat Super heated Region Calculate: Heat absorbed for 0.01 temperature drop Qsh = f (P i, t i, t o ) = m f * ΔH μ, ρ, C p, k, Re, Pr, Single phase ht tr coeff. Dittus Boelter C max, C min, η f, U ε, NTU, Q Pressure drop for the segment (Δp seg ) P i = P i Δp seg, L seg = L seg + dl T i = T o T o = T o Increment segmental length - dl Check Q>Q sh Q sum = Q sum + Q sh A Figure 4.6 Flow chart for Condenser simulation

21 69 A While X > = 1 Two Phase Region Calculate: Heat absorbed for 0.01 quality drop Q tp = f (P i, x i, x o ) = m f * ΔH μ, ρ, C p, k, σ, Re, Pr, for saturated liquid and vapour Two phase ht. tr. coeff. - Ali eqn. C max, C min, η f, U ε, NTU, Q Pressure drop for the segment (Δp seg ) P i = P i Δp seg, L seg = L seg + dl x i = x o x o = x o Check Q>Q tp Q sum = Q sum + Q tp While L cum < =TL 1 Sub cooled Region Calculate: Heat absorbed for 0.01 temperature drop, Q sh = f (P A i, t i, t o ) = m f * ΔH μ, ρ, C p, k, Re, Pr, Single phase ht. tr. coeff. Dittus Boelter C max, C min, η f, U ε, NTU, Q Pressure drop for the segment (Δp seg ) P i = P i Δp seg, L seg = L seg +dl T i = T o T o = T o 0.01 Check Q>Q sc Q sum = Q sum + Q sh Print outputs: T s,t aeo,q e, Stop Figure 4.6 Flow chart for Condenser simulation (Continued)

22 MODELING AND SIMULATION OF COMPRESSOR Modeling of compressor The following assumptions are made in the simulation of compressors. The modeled compressor cycle is an approximation of a real compressor cycle. Compression and expansion are assumed to be polytropic. The polytropic exponent is a function of the refrigerant type and compression ratio. The lubricant oil has negligible effects on the refrigerant properties. The pressure loss in the valves, and pipelines, are negligible. A compressor was modeled as a volume flow device, by using the basic thermodynamic equations. The low-pressure superheated refrigerant vapor coming out of the evaporator is compressed to the condenser pressure in the compressor. A set of equations and empirical relations were used to model the compression process. The compressor used in the present work is a swash plate type with a displacement volume of 108 cc per revolution of the compressor shaft. A swash plate compressor usually has 5 to 9 cylinders with individual pistons on one side or on either side of the connecting rod. The model was assumed to be a single cylinder compressor whose swept volume equals the total swept volume of the five-cylinder compressor. The inputs to the compressor are the evaporator outlet pressure, temperature and compressor speed. The volumetric efficiency of the compressor will be high at low speeds and low at high speeds. Since an automobile airconditioning system is tested for different speeds, an empirical equation for volumetric efficiency, as a function of speed and pressure ratio, is obtained by the curve fitting the experimental data. A flowchart detailing the calculation procedure is shown in Figure 4.7.

23 71 Start Input Data: P s, T s, P d, N Calculate: n = f (P s, T s ), h s = f (P s, T s ) T d = T s *(P d /P s )^( (n-1)/n) h d = f (T d, P d ) PR = P d /P s Voleff = f (N, PR) Density = f (P s, T s ) Calculate: m f = V d * ρ* (N/60)* η vol W c = m f *[ n/(n-1) *P s * v *( (P d /P s )^((n-1)/n)) 1] Print m f, T d, W c, η vol Stop Figure 4.7 Flowchart for compressor simulation

24 72 The work of compression is calculated from the following set of equations. The compression index n is calculated from P 2 log P1 n v 1 log v2 (4.42) The discharge temperature is calculated from T T P P n1 n - (4.43) The volumetric efficiency, pressure drop and compressor efficiency are expressed as a function of the speed and pressure ratio, based on the experimental data observed in the present work θ η vol = N PR - For M09 (4.44) For R12 (4.45) vol N PR ΔP e=5.3116e-07 N PR (4.46) ΔP c=5.442e-04 N PR (4.47) η comp = N PR - For R12 (4.48) η comp = N PR - For M09 (4.49) calculated by The mass flow rate in the compressor at any given speed is

25 73 N m f Vd vol (4.50) 60 The work of compression is given by W n n1 n n p2 p1v 1 1 p1 1 (4.51) and the compressor power is given by W P (4.52) comp Simulation of compressor Equations (4.42) to (4.48) represent the expressions used for evaluating the compressor performance. The detailed simulation procedure is given below: The evaporator outlet pressure, evaporator outlet temperature, compressor discharge pressure and compressor speed are given as input to the compressor simulation program. The index of compression is calculated. The pressures and temperatures are obtained from REFPROP software (NIST Data base). The discharge temperature is calculated. The volumetric efficiency is calculated from the expressions cited above, which was curve fitted from the experimental data.

26 74 The mass of the refrigerant circulated is calculated, and Finally the work of compression is calculated. The deliverables of the compressor simulation are the discharge temperature, mass flow rate, and compressor power. 4.5 MODELING AND SIMULATION OF TXV The following assumptions are made in simulation of TXV: The expansion process is an isenthalpic. The heat transfer from the expansion valves is negligible. An expansion device in a refrigeration system is used to expand the liquid refrigerant from the condenser pressure to the evaporator pressure. A thermostatic expansion valve maintains a constant degree of super heat in the evaporator exit. It keeps the evaporator always full of refrigerant, regardless of the changes in the cooling load. This ensures the efficient utilization of the evaporator surface even under extreme load (low/high) conditions and the safety of compressor by not allowing the liquid or the twophase mixture to enter the compressor inlet, under part load conditions Modeling of thermostatic expansion valve A thermostatic expansion valve was modeled as a throttling device in which the refrigerant expands from condenser pressure to evaporator pressure. h co = f(p co,t co ) (4.53) h ei = h f + x h fg (4.54)

27 Simulation of TXV The simulation of thermostatic expansion valve is detailed below. The inputs to the thermostatic expansion model are condenser pressure, condenser exit temperature and evaporator pressure of the refrigerant. From the condenser outlet temperature and pressure, the enthalpy of the refrigerant at the inlet of the expansion device is calculated. From the evaporator simulation the outlet quality can be calculated. With the quality and evaporator pressure and temperature the enthalpy of the mixture is calculated and compared. 4.6 INTEGRATED SYSTEM SIMULATION To avoid cumbersome calculations the domain was fairly approximated to be a simple one with the following assumptions. The property variation in all the components is onedimensional. The mass flow rate at any given speed is constant and is dependent on the performance of the compressor. The ambient temperature is constant. The ambient air is considered as dry air.

28 76 The oil present in the refrigerant is negligible influence on energy interactions There is no concentration change in the mixtures. It should be noted that the property data required by the program would be obtained from the REFPROP software as and when required. The individual components that have been simulated separately had been integrated to simulate the entire automobile air-conditioning system. The flowchart in Figure 4.8 shows the basic components and their interactions. To simplify the flowchart only the important parameters and the evaluation sequence are indicated. The detailed simulation procedure is given below: The input to the system simulation is the suction pressure, discharge pressure, compressor speed, and the suction superheat; the sub cooling and the mass flow rate are initialized. Calculate the pressure drop for the evaporator and the condenser side as a function of the suction pressure, discharge pressure and speed. The evaporator is simulated with the available data; the evaporator outlet temperature is fed as the input to the compressor. The compressor is simulated with the available data from which, the work of compression, mass flow rate and the discharge temperature are calculated.

29 77 Start Input Data: Compressor suction and discharge pressure - P s, P d compressor speed N SH =7C, SC = 5C. Calculate suction and Discharge pressure drops dp = f ( N, P d /P s ) While Sh err >0.001 While x err >0.001 While Sc err >0.001 Modify P d While mf err >0.001 Evaporator simulation: Calculate Q e, T aeo,t reo m f = m f new Modify SH Compressor simulation: Calculate η vol, m f, W c, T d mf err = abs(m fnew m f )/m fnew Condenser simulation: Calculate Q c, T aco Modify x Check Sub cooling TXV Simulation Check Q e +W c = Q c Print Outputs Stop Figure 4.8 Flowchart for the integrated system simulation

30 78 The new mass flow rate is compared with the initialized mass flow rate and it is successively substituted till convergence is achieved. With the new mass flow rate, discharge pressure and temperature, the condenser heat transfer rate is simulated, and the condenser outlet temperature and sub cooling are calculated. The sub cooling obtained is compared with the initialized value. The discharge pressure is modified to match the sub cooling of the condenser. From the converged sub cooling temperature and condenser pressure, the enthalpy can be found. This enthalpy is used to verify the evaporator inlet pressure and the quality obtained from the evaporator simulation. Finally, the heat input in the form of the evaporator heat load and compressor work is compared with the heat rejection in the condenser. The superheat in the evaporator is altered till convergence is achieved. Once the system is balanced, the outputs of the discharge temperature, the heat absorbed in the evaporator, compressor power and the COP are delivered. All the components are simulated individually and integrated to simulate the total system. The simulated values are compared with the experimental results and analyzed.